Face numbers of sequentially Cohen–Macaulay complexes and Betti numbers of componentwise linear ideals

  • Karim A. Adiprasito

    Hebrew University Jerusalem, Israel
  • Anders Björner

    Royal Institute of Technology, Stockholm, Sweden
  • Afshin Goodarzi

    Freie Universität Berlin, Germany

Abstract

A numerical characterization is given of the -triangles of sequentially Cohen–Macaulay simplicial complexes. This result determines the number of faces of various dimensions and codimensions that are possible in such a complex, generalizing the classical Macaulay–Stanley theorem to the nonpure case. Moreover, we characterize the possible Betti tables of componentwise linear ideals. A key tool in our investigation is a bijection between shifted multicomplexes of degree and shifted pure -dimensional simplicial complexes

Cite this article

Karim A. Adiprasito, Anders Björner, Afshin Goodarzi, Face numbers of sequentially Cohen–Macaulay complexes and Betti numbers of componentwise linear ideals. J. Eur. Math. Soc. 19 (2017), no. 12, pp. 3851–3865

DOI 10.4171/JEMS/755